Reviewing Yield Criteria in Plasticity Theory

Mathematical plasticity theory assumes in many cases that deformation occurs without a change in volume. A yield surface, which limits elasticity under arbitrary combinations of stresses, is thus the function of the deviatoric components of the stress tensor. The yield criteria define this limit surface in the principal stress space. The commonly accepted criteria are Tresca, von Mises and Schmidt-Ishlinsky. Nowadays, they are not sufficient for modelling of real material behaviour in critical components and are generalized in the different ways. Numerous criteria proposed over the last 150 years are hardly used because their utility is not obvious. In addition, the cost of material testing, parameter adjustment and complexity of criterion implementation often outweighs the benefits of accurate material description. Furthermore, there is no clear procedure for selecting the best criterion for a particular application. This paper summarises frequently discussed yield criteria and assigns them to five derivation paths. Based on the introduced nomenclature, a verification standard for these criteria is outlined and the number of yield criteria is reduced to a few manageable cases. The criteria are classified into criteria of trigonal and hexagonal symmetry in the π-plane with C0- and C1-continuity for solving various problems. Four missing criteria are identified, but their mathematical formulation is still subject to discussion. Four other yield criteria, which best meet plausibility requirements, are recommended instead. These criteria are suitable for all pressure-insensitive isotropic materials. The development and selection of particular criteria for certain groups of materials are therefore no longer necessary.